Notes on Testing Symmetry Conditions between Factor Demand Equations

A potentially important econometric test of profit maximization by producers is a test on the implied relationships among coefficients of different factor demand equations; i.e., a test for symmetry between factor demand equations. In this paper such a test procedure is developed and implemented for two lower income economies and implications are drawn for future work. In particular, an economy is disaggregated into the three sectors which are believed to have considerably different production functions-the primary or agricultural sector, the secondary or manufacturing sector, and the tertiary or service sector. Cobb-Douglas production functions for these sectors are then specified and the utilization of factor inputs is determined by static profit maximization. Finally, the resulting equations are estimated with data from Colombia and pre-war Japan in order to ascertain whether such a model is consistent with the empirical results. The conclusion from the tests is that the model is completely refuted by our data. The result implies that at least one of the following is the source of the rejection: (1) Firms are not profit maximizing in less developed countries, at least in the static sense; (2) the functional forms for the production functions or product demand functions are inappropriate specifications; (3) the measurement of the cost of capital by its supply price is fallacious; (4) the basic data are subject to large and important errors; or (5) the data are on too high a level of aggregation. In the last section, major implications of these results for further research are indicated

Economics · Factor (programming language) · Geometry · Physics · Symmetry (geometry) · Theoretical physics · Computer Science · Economic theories and models · Mathematics